A and B can do a work in 45 days and 40 days respectively. They started working but A left after some days and B alone complete the remaining work in 23 days. After how many days did A leave ?
Answer & explanation
Correct answer: option 4
A can do a work in time = 45 days
A's one day work = 1/45
B can do a work in time = 40 days
B's one day work = 1/40
If they work together, one day work of A and B = 1/45 + 1/40 = 8+9/360 = 17/360
Let they work for x days initially,
A and B x days work = 17x/360
Remaining work = 1- 17x/360 = (360-17x)/360
B alone does (360-17x)/360 in time = 23 days
Also, B's 23 days work = 23/40
⇒ (360-17x)/360 = 23/40
360-17x = 9*23
17x = 360-207
x = 153/17 = 9 days
The correct answer is option (4) : 9